hyperbola

[hyunah]

how do we graph a hyperbola with an inquality? (eg. x^2/16 +y^2/9 > 1)

[TrueTears]

a good way is to test a point, e.g., does (0,0) satisfy the strict inequality? If not, what does that say about the 'region' where (0,0) lies in?

[hongkyho]

Let's assume that the shaded area is the region required.

How I would usually tackle these questions is to first ignore the inequality sign and replace it with an equals sign. Then I would draw the graph accordingly.

The next step is to figure out which region do I shade, inside the oval or outside. I would do this by using a point (it can be any point like (1,1)!) and see if it holds true for the orginal inequality. If it does, then the region that that point lies in is the region you shade. If it does not hold true, then you shade the other region.

Also, if I'm not mistaken, that is an ellipse, not a hyperbola.

Hope this helped.

Edit: Beaten by TrueTears